KVPY SX SB Exam 2015 Question Paper

Question : 33 of 120

Marks: +1, -0

A donor atom in a semiconductor has a loosely bound electron. The orbit of this electron is considerably affected by the semiconductor material but behaves in many ways like an electron orbiting a hydrogen nucleus. Given that the electron has an effective mass of 0.07 m

_e

, (where me is mass of the free electron) and the space in which it moves has a permittivity 13

ε_0

, then the radius of the electron's lowermost energy orbit will be close to (The Bohr radius of the hydrogen atom is 0.53 Å)

0.53 Å
243 Å
10 Å
100 Å

Validate

Solution:

From Bohr postulates

{kze^2}/r^2={mv^2}/r

….(i)

mvr = {nh}/{2π}

….(ii)
⇒

v=e^2/{2ε_0h}z/n

r={nh}/{2 πmv}

r={nh}/{2 πm(e^2/{2ε_0h})(z/n)}

r=({{ε_0h^2}/{πme^2}})(n^2/z)

r=r_0n^2/z

Because the medium of permittivity

ε = 13 ε_0

effective mass m = 0.07 m

_e

r={13r_0}/0.07\;n^2/z

At ground state (n = 1, assuming like H atom, z = 1)

r=13/0.07(0.53 Å

⇒

r ≈ 100 \Å

Go to Question:

Prev Question

Next Question